Robbie Willmott's goal was not enough as Cambridge United suffered their first defeat under Richard Money.
Jonathan Hedge was forced to push away a low long-range drive from Jack Parkinson early on while Billy Knott fired tamely wide as Woking started brightly.
Jonathon Thorpe fired wide with an angled effort at the other end, but Bubb gave the hosts the edge on 19 minutes by nodding home unmarked from Kevin Betsy's cross.
Willmott had a low shot from the edge of the area saved by home keeper Sam Beasant soon after while Bubb should have bagged a second, only to mis-hit with the goal gaping from Gavin McCallum's ball in from the right.
Rory McAuley went close to an equaliser with a header from Danny Andrew's corner just before half time but Betsy doubled Woking's lead on the hour after taking advantage of poor defending to fire home, before Willmott pulled one back with a near post finish four minutes later to give United hope.
United piled the pressure on, but the closest they came to an equaliser was Andy Pugh diverting fellow substitute Ricky Wellard's low drive on to the post.
21:40 Full-Time: Woking 2-1 Cambridge United. Cambridge huffed and puffed in the latter stages but the damage had been done earlier with some below par defending.
21:36 Adriano Moke is caught offside when an attack was looking promising.
21:34 Six minutes of injury time to be played.
21:32 Danny Andrew wins another corner, it runs through to Berry but his shot ends up in the stand.
21:31 Woking make their final change as Gavin McCallum is replaced by Adam Doyle.
21:29 Woking are rocking here, as Cambridge win yet another corner but it comes to nothing.
21:28 Moke wins another corner as the U's pile on the pressure, Woking just about do enough to get this one away.
21:26 Adriano Moke sees his shot deflected wide for a corner, Andrew takes and it falls to Wellard who fires a shot goal wards but Beasant smothers.
21:24 Gash heads the resulting free kick straight at the keeper.
21:24 Pugh is fouled and McNerney is booked.
21:22 Another corner for Cambridge and again Woking head clear, it comes back in but Gash heads over.
21:22 Andy Pugh has a shot deflected against the post, and then out for a corner. Woking defend.
21:21 Parkinson this time has a shot that goes well wide. Cambridge need to do better to win the second ball.
21:19 Dean Sinclair shoots high and wide after some poor defending from Cambridge United.
21:18 Bradley Bubb is replaced by Brett Williams.
21:12 Dean Sinclair replaces the injured Billy Knott.
21:10 A break in play at the moment as Knott receives treatment.
21:08 The U's win another corner which Luke Berry heads wide, the U's looking better at the moment.
21:07 GOAL: Woking 2-1 Cambridge United. Andy Pugh won a corner which Andrew delivered and Robbie Willmott heads home to claim his first goal of the season.
21:05 Cambridge make their final change now as Andy Pugh replaces Tom Elliott.
21:03 GOAL: Woking 2-0 Cambridge United. Kevin Betsy makes it two after playing a one two with Bubb and slotting home. Poor defending from the U's it has to be said.
21:02 Ricky Wellard replaces Tom Shaw as Richard Money makes his second change.
21:00 Great save from Hedge, diving full stretch to his right to deny Sawyer, corner to Woking. United defend and it results in a goal kick.
20:57 Half chance for United as Berry finds Elliott but the striker can't direct his effort towards goal.
20:57 Cambridge make the first change of the evening as Adriano Moke replaces Jarvis.
20:55 Lee sawyer fouls Berry and is the second man into the book.
20:48 Cambridge kick off the second half.
20:48 The attendance tonight is 1,420 with 199 fans from Cambridge.
20.33 Half-Time: Woking 1-0 Cambridge United. The U's trail by one goal at the break courtesy of Bradley Bubb's 19th minute header. Richard Money will expect to see his side provide a more attacking threat after the interval.
20:31 Cambridge win a corner here late in the first half, Andrew delivers and McAuley heads just wide. The fourth official indicates two minutes of added time to be played.
20:27 Woking win a dubious looking free kick, Coulson just about does enough to get it clear.
20:19 Mike Sestor is booked for a foul on Thorpe.
20:17 Another corner for Cambridge now which Andrew again delivers, but Woking defend well once again.
20:14 Danny Andrew delivers a free kick, which is headed out for a corner which Woking deal with.
20:13 Bubb should have scored, big let off. The U's defence looking a little shaky here.
20:12 A Woking corner now, driven in but the U's clear well.
20:10 Tom Elliott has a shot blocked and it's out for a corner. Andrew takes, and it eventually falls to McAuley who has a shot saved.
20:06 GOAL: Woking 1-0 Cambridge United. Betsy has time on the right to cross and Bradley Bubb heads home. Danny Andrew could perhaps have done better there to prevent the cross.
20:05 Great football from Cambridge, finishing with a good cross from Thorpe but Beasant collects with Tom Elliott looming.
19:59 A quick break down the right from the U's ends with Shaw shooting just wide, that's the best chance so far.
19:58 Another wayward effort from the hosts.
19:57 Berry and Willmott combine well, Robbie pulls the ball back on the by-line but Sam Beasant smothers.
19:56 Billy Knott shoots well wide.
19:55 Elliott over runs the ball, should have passed to Gash earlier, the big striker is looking for a foul but the ref waves it away.
19:51 A good start from the hosts.
19:50 A long shot from Parkinson is palmed away for a corner from Hedge, Berry heads clear.
19:48 Woking win a corner, Elliott heads it clear, a cross comes in but Hedge catches comfortably.
19:46 Woking kick off.
19:20 Teams: Woking: Sam Beasant, Mike Cestor, Mark Ricketts, Joe McNerney, Brett Johnson, Jack Parkinson, Lee Sawyer, Billy Knott, Kevin Betsy, Bradley Bubb, Gavin McCallum. Subs: Andy Little, Adam Doyle, Dean Sinclair, Brett Williams, Loick Pires.
Cambridge: Jonathan Hedge, Danny Andrew, Josh Coulson, Rory McAuley, Jonathon Thorpe, Robbie Willmott, Luke Berry, Tom Shaw, Rossi Jarvis, Tom Elliott, Michael Gash. Subs: Craig Ross, Michael Wylde, Ricky Wellard, Adriano Moke, Andy Pugh.
19:00 Good evening guys and girls and welcome along for tonight's Blue Square premier clash between Woking and Cambridge.
Richard Money takes charge of his first away game as the U's manager following the fantastic 4-1 victory over Mansfield last Saturday, and a win tonight will make it three wins in a row for Cambridge.
Team news to follow.
Match report provided by cambridgeunited.com reporter Sam Line.